This continuity is merely the name for the aggregate of a variety of properties of events in connexion with the relation of extension.
In the first place, this relation is transitive; secondly, every event contains other events as parts of itself; thirdly every event is a part of other events; fourthly given any two finite events there are events each of which contains both of them as parts; and fifthly there is a special relation between events which I term 'junction.' Two events have junction when there is a third event of which both events are parts, and which is such that no part of it is separated from both of the two given events.

Thus two events with junction make up exactly one event which is in a sense their sum.
Only certain pairs of events have this property.

In general any event containing two events also contains parts which are separated from both events.
There is an alternative definition of the junction of two events which I have adopted in my recent book[7].

Two events have junction when there is a third event such that (i) it overlaps both events and (ii) it has no part which is separated from both the given events.

If either of these alternative definitions is adopted as the definition of junction, the other definition appears as an axiom respecting the character of junction as we know it in nature.